Why is R = {(1,2), (2,3)} not transitive on A = {1,2,3}?
Answer and explanation
Correct answer: क्योंकि (1,3) ∉ R
Transitivity requires that whenever (a,b) and (b,c) are in R, the pair (a,c) must also be in R. In this relation, (1,2) and (2,3) provide a valid two-step chain, so transitivity demands (1,3). Because (1,3) is not in R, the condition fails. The missing pairs (2,1) or (1,1) concern other properties, and R is certainly not all of A × A. Thus A is correct.
Frequently asked questions
What is the correct answer to this question?
क्योंकि (1,3) ∉ R
Why is this the correct answer?
Transitivity requires that whenever (a,b) and (b,c) are in R, the pair (a,c) must also be in R. In this relation, (1,2) and (2,3) provide a valid two-step chain, so transitivity demands (1,3). Because (1,3) is not in R, the condition fails. The missing pairs (2,1) or (1,1) concern other properties, and R is certainly not all of A × A. Thus A is correct.
Which subject and chapter does this question cover?
This is a Class 11 Mathematics question. Chapter: Relations and Functions. Topic: Relations.
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